Method and system of transmitting independent data from transmitters to receivers

ABSTRACT

Disclosed is a method and system to transmit independent data by at least two transmitters to corresponding at least two receivers. The method includes obtaining, at a first transmitter, a first ternary sequence from a first base ternary sequence corresponding to a first set of data-symbols, and obtaining, at a second transmitter, a second ternary sequence from a second base ternary sequence corresponding to a second set of data-symbols. The method also includes transmitting, from the first transmitter, the first ternary sequence to a first set of receivers associated with the first transmitter. The method transmits, from the second transmitter, the second ternary sequence to a second set of receivers associated with the second transmitter.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. § 119(a) of IndianPatent Application No. 5484/CHE/2015 filed on Oct. 13, 2015, and IndianPatent Application No. 5484/CHE/2015 filed on Aug. 9, 2016 in theIntellectual Property India, and claims the benefit under 35 U.S.C. §119(a) of Korean Patent Application No. 10-2016-0123091 filed on Sep.26, 2016 in the Korean Intellectual Property Office, the entiredisclosures of which are incorporated herein by reference for allpurposes.

BACKGROUND 1. Field

The following description relates to a communication system, and moreparticularly, to a mechanism of transmitting independent data from atleast two transmitters to corresponding at least two receivers.

2. Description of Related Art

Short range low power wireless networks, such as Wireless Personal AreaNetwork (WPAN) and Wireless Body Area Network (WBAN), employ wirelessdevices with a small form factor and are required to conserve theirbattery life. Therefore, the wireless devices need to operate atrelatively low data rates and consume low power. These constraintsdefined for short range low power networks limit transmission to lowerorder modulation schemes, such as On-Off Keying (OOK), Frequency ShiftKeying (FSK) and Binary Phase Shift Keying (BPSK).

The short range low power wireless networks employ both coherent andnon-coherent forms of reception depending on the range/signal-to-noiseratio (SNR) requirements. In general, a transmission format of a signaltransmitted from a transmitter is arranged to correspond to and bereadable and be able to be processed by a corresponding receiver. Forinstance, for coherent reception over a binary alphabet (0, 1) as inOOK, a transmission signal is configured with the same binary alphabet(0, 1). Similarly, for transmission to a coherent receiver over aternary alphabet {−1, 0, 1}, a transmission signal is configured withthe ternary alphabet.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used as an aid in determining the scope of the claimed subjectmatter.

In accordance with an embodiment, there is provided a method to transmitindependent data, the method including: obtaining, at a firsttransmitter, a first ternary sequence from a first base ternary sequencecorresponding to a first set of data-symbols; obtaining, at a secondtransmitter, a second ternary sequence from a second base ternarysequence corresponding to a second set of data-symbols; transmitting,from the first transmitter, the first ternary sequence to a first set ofreceivers associated with the first transmitter; and transmitting, fromthe second transmitter, the second ternary sequence to a second set ofreceivers associated with the second transmitter.

The first base ternary sequence may include a predefined length andretrieved at the first transmitter.

The second base ternary sequence may include a predefined length and maybe retrieved at the second transmitter.

The first ternary sequence may be obtained as a cyclic shift of thefirst base ternary sequence, and the cyclic shift may correspond to adata-symbol to be transmitted from the first transmitter and may bedetermined based on a one-to-one mapping.

The second ternary sequence may be obtained as a cyclic shift of thesecond base ternary sequence, and the cyclic shift may correspond to adata-symbol to be transmitted from the second transmitter and may bedetermined based on a one-to-one mapping.

The first base ternary sequence may be generated by: obtaining a firstm-sequence of a period N−1; obtaining a first perfect ternary sequencefrom the first m-sequence; and appending a zero to a run of all zeros inthe first perfect ternary sequence.

The second base ternary sequence may be generated by: obtaining a secondm-sequence of a period N−1 as a decimation of a first m-sequence used togenerate the first ternary sequence; obtaining a second perfect ternarysequence from the second m-sequence; and appending a zero to a run ofall zeros in the second perfect ternary sequence.

The first perfect ternary sequence may be generated from the firstm-sequence by: obtaining a preferred pair of m-sequences from the firstm-sequence; obtaining a first correlation sequence of the preferredpair, the correlation sequence being obtained as a cross-correlationfunction between two m-sequences of the preferred pair; obtaining afirst offset correlation sequence from the first correlation sequence;and generating the first perfect ternary sequence based on the firstoffset correlation sequence.

The second perfect ternary sequence may be generated from the secondm-sequence by: obtaining a preferred pair of m-sequences from the secondm-sequence; obtaining a second correlation sequence of the preferredpair, the correlation sequence being obtained as a cross-correlationfunction between two m-sequences of the preferred pair; obtaining asecond offset correlation sequence from the second correlation sequence;and generating the second perfect ternary sequence based on the secondoffset correlation sequence.

The first set of receivers may include a first non-coherent receiver anda first coherent receiver associated with the first transmitter, and thesecond set of receivers may include a second non-coherent receiver and asecond coherent receiver associated with the second transmitter.

The method may also include: receiving, at the first set of receivers,the first ternary sequence transmitted from the first transmitter;receiving, at the second set of receivers, the second ternary sequencetransmitted from the second transmitter; demodulating, at the firstcoherent receiver, the first ternary sequence by correlating the firstternary sequence with all cyclic shifts of a conjugate sequence obtainedfrom the first base ternary sequence; and demodulating, at the firstnon-coherent receiver, the first ternary sequence by correlating thefirst ternary sequence with all cyclic shifts of a conjugate sequenceobtained from an absolute value of the first base ternary sequence.

The method may also include: demodulating, at the second coherentreceiver, the second ternary sequence by correlating the second ternarysequence with all cyclic shifts of a conjugate sequence obtained fromthe second base ternary sequence; and demodulating, at the secondnon-coherent receiver, the second ternary sequence by correlating thesecond ternary sequence with all cyclic shifts of a conjugate sequenceobtained from an absolute value of the second base ternary sequence.

The method may also include: detecting, at the first set of receivers, adata-symbol transmitted from the first transmitter by identifying afirst single cyclic shift corresponding to a maximum correlation valueamong all cyclic shifts; detecting, at the second set of receivers, adata-symbol transmitted from the second transmitter by identifying asecond single cyclic shift corresponding to the maximum correlationvalue among all cyclic shifts; obtaining, at the first set of receivers,each of the data-symbols corresponding to the first transmitter from thefirst single cyclic shift using an inverse of the one-to-one mapping;and obtaining, at the second set of receivers, each of the data-symbolscorresponding to the second transmitter from the second single cyclicshift using the inverse of the one-to-one mapping.

The conjugate sequence may be obtained by replacing numeric ‘0’ withnumeric ‘1’.

The absolute value of the first base ternary sequence and an absolutevalue of the second base ternary sequence are obtained by replacingnumeric ‘−1’ of the first base ternary sequence and by replacing numeric‘−1’ of the second base ternary sequence with numeric ‘1’.

Data to be transmitted may be divided into the first set of data-symbolswith a predefined length and the second set of data-symbols with thepredefined length.

In accordance with a further embodiment, there is provided a system fortransmitting independent data, including: a first transmitter configuredto obtain a first ternary sequence from a first base ternary sequencecorresponding to a first set of data-symbols; and a second transmitterconfigured to obtain a second ternary sequence from a second baseternary sequence corresponding to a second set of data-symbols, whereinthe first transmitter may be further configured to transmit the firstternary sequence to a first set of receivers associated with the firsttransmitter, and the second transmitter may be further configured totransmit the second ternary sequence to a second set of receiversassociated with the second transmitter.

The first base ternary sequence may include a predefined lengthretrieved at the first transmitter.

The second base ternary sequence may include the predefined lengthretrieved at the second transmitter.

The first ternary sequence may be obtained as a cyclic shift of thefirst base ternary sequence, and the cyclic shift corresponds to adata-symbol to be transmitted from the first transmitter and may bedetermined based on a one-to-one mapping.

The second ternary sequence may be obtained as a cyclic shift of thesecond base ternary sequence, and the cyclic shift corresponds to adata-symbol to be transmitted from the second transmitter and may bedetermined based on a one-to-one mapping.

The first base ternary sequence may be generated by obtaining a firstm-sequence of a period N−1, obtaining a first perfect ternary sequencefrom the first m-sequence, and appending a zero to a run of all zeros inthe first perfect ternary sequence.

The second base ternary sequence may be generated by obtaining a secondm-sequence of a period N−1 as a decimation of a first m-sequence used togenerate the first ternary sequence, obtaining a second perfect ternarysequence from the second m-sequence, and appending a zero to a run ofall zeros in the second perfect ternary sequence.

The first perfect ternary sequence may be generated from the firstm-sequence by obtaining a preferred pair of m-sequences from the firstm-sequence, obtaining a first correlation sequence of the preferredpair, the correlation sequence being obtained as a cross-correlationfunction between two m-sequences of the preferred pair, obtaining afirst offset correlation sequence from the first correlation sequence,and generating the first perfect ternary sequence based on the firstoffset correlation sequence.

The second perfect ternary sequence may be generated from the secondm-sequence by obtaining a preferred pair of m-sequences from the secondm-sequence, obtaining a second correlation sequence of the preferredpair, the correlation sequence being obtained as a cross-correlationfunction between two m-sequences of the preferred pair, obtaining asecond offset correlation sequence from the second correlation sequence,and generating the second perfect ternary sequence based on the secondoffset correlation sequence.

The first set of receivers may include a first non-coherent receiver anda first coherent receiver associated with the first transmitter, and thesecond set of receivers may include a second non-coherent receiver and asecond coherent receiver associated with the second transmitter.

The system may be further configured to receive, using the first set ofreceivers, the first ternary sequence transmitted from the firsttransmitter, receive, using the second set of receivers, the secondternary sequence transmitted from the second transmitter, demodulate,using the first coherent receiver, the first ternary sequence bycorrelating the first ternary sequence with all cyclic shifts of aconjugate sequence obtained from the first base ternary sequence, anddemodulate, using the first non-coherent receiver, the first ternarysequence by correlating the first ternary sequence with all cyclicshifts of a conjugate sequence obtained from an absolute value of thefirst base ternary sequence.

The system may be further configured to: demodulate, using the secondcoherent receiver, the second ternary sequence by correlating the secondternary sequence with all cyclic shifts of a conjugate sequence obtainedfrom the second base ternary sequence, and demodulate, using the secondnon-coherent receiver, the second ternary sequence by correlating thesecond ternary sequence with all cyclic shifts of a conjugate sequenceobtained from an absolute value of the second base ternary sequence.

The system may be further configured to: detect, using the first set ofreceivers, a data-symbol transmitted from the first transmitter byidentifying a first single cyclic shift corresponding to a maximumcorrelation value among all cyclic shifts, detect, using the second setof receivers, a data-symbol transmitted from the second transmitter byidentifying a second single cyclic shift corresponding to the maximumcorrelation value among all cyclic shifts, obtain, using the first setof receivers, each of the data-symbols corresponding to the firsttransmitter from the first single cyclic shift, and obtain, using thesecond set of receivers, each of the data-symbols corresponding to thesecond transmitter from the second single cyclic shift using an inverseof the one-to-one mapping.

The conjugate sequence may be obtained by replacing numeric ‘0’ withnumeric ‘1’.

The absolute value of the first base ternary sequence and an absolutevalue of the second base ternary sequence are obtained by replacingnumeric ‘−1’ of the first base ternary sequence and by replacing numeric‘−1’ of the second base ternary sequence with numeric ‘1’.

Data to be transmitted may be divided into the first set of data-symbolswith a predefined length and the second set of data-symbols with thepredefined length.

In accordance with a further embodiment, there is provided a method toreceive independent data, the method including: a first coherentreceiver configured to demodulate a first ternary sequence received froma first transmitter by correlating the first ternary sequence with allcyclic shifts of a conjugate sequence obtained from a first base ternarysequence corresponding to a first set of data-symbols; a firstnon-coherent receiver configured to demodulate the first ternarysequence by correlating the first ternary sequence with all cyclicshifts of a conjugate sequence obtained from an absolute value of thefirst base ternary sequence; a second coherent receiver configured todemodulate a second ternary sequence received from a second transmitterby correlating the second ternary sequence with all cyclic shifts of aconjugate sequence obtained from a second base ternary sequencecorresponding to a second set of data-symbols; and a second non-coherentreceiver configured to demodulate the second ternary sequence bycorrelating the second ternary sequence with all cyclic shifts of aconjugate sequence obtained from an absolute value of the second baseternary sequence.

The first set of data-symbols may be detected by identifying a firstsingle cyclic shift corresponding to a maximum correlation value amongall of the cyclic shifts of the conjugate sequence obtained from thefirst base ternary sequence.

The second set of data-symbols may be detected by identifying a secondsingle cyclic shift corresponding to a maximum correlation value amongall of the cyclic shifts of the conjugate sequence obtained from thesecond base ternary sequence.

The first set of data-symbols may include a first predefined length andthe second set of data-symbols may include a second predefined length.

Other features and aspects will be apparent from the following detaileddescription, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a communication system, inaccordance with an embodiment;

FIG. 2 is a diagram illustrating various operations of a transmitter, acoherent receiver, and a non-coherent receiver in the communicationsystem, in accordance with an embodiment;

FIG. 3 is a flowchart illustrating an example of a method transmittingindependent data by at least two transmitters to corresponding at leasttwo receivers, in accordance with an embodiment;

FIG. 4A is a flowchart illustrating an example of a method to obtain afirst base ternary sequence, in accordance with an embodiment;

FIG. 4B is a flowchart illustrating an example of a method to obtain asecond base ternary sequence, in accordance with an embodiment;

FIG. 5A is a flowchart illustrating an example of a method to generate afirst perfect ternary sequence, in accordance with an embodiment;

FIG. 5B is a flowchart illustrating an example of a method to generate asecond perfect ternary sequence, in accordance with an embodiment;

FIG. 6 is a flowchart illustrating an example of a method to identifydata represented by a received ternary sequence at a set of receivers,in accordance with an embodiment;

FIGS. 7A and 7B are graphs showing examples of an autocorrelationproperty of a first base ternary sequence, in accordance with anembodiment;

FIGS. 8A and 8B are graphs showing examples of an autocorrelationproperty of a second base ternary sequence, in accordance with anembodiment; and

FIGS. 9A and 9B are graphs showing examples of a correlation between afirst base ternary sequence and a second base ternary sequence, inaccordance with an embodiment.

Throughout the drawings and the detailed description, unless otherwisedescribed or provided, the same drawing reference numerals will beunderstood to refer to the same elements, features, and structures. Thedrawings may not be to scale, and the relative size, proportions, anddepiction of elements in the drawings may be exaggerated for clarity,illustration, and convenience.

DETAILED DESCRIPTION

The following detailed description is provided to assist the reader ingaining a comprehensive understanding of the methods, apparatuses,and/or systems described herein. However, various changes,modifications, and equivalents of the methods, apparatuses, and/orsystems described herein will be apparent after an understanding of thedisclosure of this application. The sequences of operations describedherein are merely examples, and are not limited to those set forthherein, but may be changed as will be apparent after an understanding ofthe disclosure of this application, with the exception of operationsnecessarily occurring in a certain order. Also, descriptions offunctions and constructions that are well known in the art may beomitted for increased clarity and conciseness.

The features described herein may be embodied in different forms, andare not to be construed as being limited to the examples describedherein. Rather, the examples described herein have been provided so thatthis disclosure will be thorough and complete, and will convey the fullscope of the disclosure after an understanding of the disclosure of thisapplication.

The examples herein and the various features and advantageous detailsthereof are explained more fully with reference to the non-limitingexamples that are illustrated in the accompanying drawings and detailedin the following description. Descriptions of well-known components andprocessing techniques are omitted so as to not unnecessarily obscure theexamples herein. Also, the various examples described herein are notnecessarily mutually exclusive, as some examples can be combined withone or more other examples to form new examples. The term “or” as usedherein refers to a non-exclusive or, unless otherwise indicated. Theexamples used herein are intended merely to facilitate an understandingof ways in which the examples herein can be practiced and to furtherenable to practice the examples herein. Accordingly, the examples shouldnot be construed as limiting the scope of the examples herein.

As used herein, the term “and/or” includes any one and any combinationof any two or more of the associated listed items.

Although terms such as “first,” “second,” and “third” may be used hereinto describe various members, components, regions, layers, or sections,these members, components, regions, layers, or sections are not to belimited by these terms. Rather, these terms are only used to distinguishone member, component, region, layer, or section from another member,component, region, layer, or section. Thus, a first member, component,region, layer, or section referred to in examples described herein mayalso be referred to as a second member, component, region, layer, orsection without departing from the teachings of the examples.

Spatially relative terms such as “above,” “upper,” “below,” and “lower”may be used herein for ease of description to describe one element'srelationship to another element as shown in the figures. Such spatiallyrelative terms are intended to encompass different orientations of thedevice in use or operation in addition to the orientation depicted inthe figures. For example, if the device in the figures is turned over,an element described as being “above” or “upper” relative to anotherelement will then be “below” or “lower” relative to the other element.Thus, the term “above” encompasses both the above and below orientationsdepending on the spatial orientation of the device. The device may alsobe oriented in other ways (for example, rotated 90 degrees or at otherorientations), and the spatially relative terms used herein are to beinterpreted accordingly.

The terminology used herein is for describing various examples only, andis not to be used to limit the disclosure. The articles “a,” “an,” and“the” are intended to include the plural forms as well, unless thecontext clearly indicates otherwise. The terms “comprises,” “includes,”and “has” specify the presence of stated features, numbers, operations,members, elements, and/or combinations thereof, but do not preclude thepresence or addition of one or more other features, numbers, operations,members, elements, and/or combinations thereof.

Due to manufacturing techniques and/or tolerances, variations of theshapes shown in the drawings may occur. Thus, the examples describedherein are not limited to the specific shapes shown in the drawings, butinclude changes in shape that occur during manufacturing.

The features of the examples described herein may be combined in variousways as will be apparent after an understanding of the disclosure ofthis application. Further, although the examples described herein have avariety of configurations, other configurations are possible as will beapparent after an understanding of the disclosure of this application.

In accordance with an embodiment, there is provided a method andcorresponding apparatus that transmits independent data from at leasttwo transmitters to corresponding at least two receivers. The method andcorresponding apparatus include obtaining, at a first transmitter of thetwo transmitters, a first ternary sequence from a first base ternarysequence corresponding to a first set of data-symbols. The first set ofdata-symbols includes a predefined length. Further, the method andcorresponding apparatus include obtaining, at a second transmitter ofthe two transmitters, a second ternary sequence from a second baseternary sequence corresponding to a second set of data-symbols. Thesecond set of data-symbols includes the predefined length. Further, themethod and corresponding apparatus include transmitting, at the firsttransmitter, the first ternary sequence to a first set of receivers. Thefirst set of receivers is associated with the first transmitter.Furthermore, the method and corresponding apparatus includetransmitting, at the second transmitter, the second ternary sequence toa second set of receivers. The second set of receivers is associatedwith the second transmitter.

Unlike the conventional system and method, in accordance with anembodiment, the method and corresponding apparatus utilize ternarysequences to support two independent communication links in acommunication system. The method and corresponding apparatus areconfigured such that the interference between two transmitters should beas low as possible. The method and corresponding apparatus reduce thepower consumption of transmitters and receivers in an electronic device,cost, and a complexity in a configuration of the transmitters and thereceivers in the electronic device.

Hereinafter, the examples will be described with reference to FIGS. 1through 9. Here, like reference numerals refer to like elementsthroughout.

FIG. 1 is a block diagram illustrating an example of a communicationsystem, in accordance with an embodiment.

Referring to FIG. 1, a communication system 100 includes a firsttransmitter 102 a, a second transmitter 102 b, a first coherent receiver104 a, a second coherent receiver 104 c, a first non-coherent receiver104 b, and a second non-coherent receiver 104 d. The communicationsystem 100 is configured to transmit independent data from transmittersto corresponding receivers, for example, the first coherent receiver 104a and the second non-coherent receiver 104 d using the two transmitters,for example, the first transmitter 102 a and the second transmitter 102b.

Data to be transmitted is divided into a first set of data-symbols witha predefined length and a second set of data-symbols with a predefinedlength. In one embodiment, the communication system 100 divides the datato be transmitted at the first transmitter 102, at the secondtransmitter 102 b, or at a processor within the communication system100. In accordance with an embodiment, the length of the first set ofdata-symbols and the length of the second set of data-symbols may be thesame or may be different from each other. The first transmitter 102 a isconfigured to obtain a first ternary sequence from a first base ternarysequence corresponding to the first set of data-symbols. In one example,the first base ternary sequence with a predefined length N is retrievedat the first transmitter 102 a.

In one example, the first base ternary sequence is generated byobtaining a first (maximal length sequence) m-sequence of a period N−1,by obtaining a first perfect ternary sequence from the first m-sequence,and by appending a zero to a run of all zeros in the first perfectternary sequence.

In one example, the first perfect ternary sequence is obtained byobtaining a preferred pair of m-sequences from the first m-sequence, andby obtaining a first correlation sequence from the preferred pair ofm-sequences. Here, the correlation sequence is obtained as across-correlation function between two m-sequences of the preferred pairof m-sequences from the first m-sequence. Further, a first offsetcorrelation sequence is obtained from the first correlation sequence.The first perfect ternary sequence is generated based on the firstoffset correlation sequence.

In one example, the first ternary sequence is obtained as a cyclic shiftof the first base ternary sequence. The cyclic shift corresponds to adata-symbol to be transmitted from the first transmitter 102 a, and thecyclic shift is determined based on a mapping procedure, for example, aone-to-one mapping.

The second transmitter 102 b is configured to obtain a second ternarysequence from a second base ternary sequence corresponding to a secondset of data-symbols. The second set of data-symbols has the predefinedlength. In an example, the second base ternary sequence with apredefined length N is retrieved at the second transmitter 102 b.

In one example, the second base ternary sequence is generated byobtaining a second m-sequence of a period N−1 as a predefined decimationof the first m-sequence used to generate the first ternary sequence, byobtaining a second perfect ternary sequence from the second m-sequence,and by appending a zero to a run of all zeros in the second perfectternary sequence.

In one example, the second perfect ternary sequence is obtained byobtaining a preferred pair of m-sequences from the second m-sequence,and by obtaining a second correlation sequence of the preferred pair.The correlation sequence is obtained as a cross-correlation functionbetween two m-sequences of the preferred pair, which is obtained fromthe second m-sequence. Further, a second offset correlation sequence isobtained from the second correlation sequence. The second perfectternary sequence is generated based on the second offset correlationsequence.

In one example, the second ternary sequence is obtained as a cyclicshift of the second base ternary sequence. The cyclic shift correspondsto a data-symbol to be transmitted from the second transmitter 102 b andthe cyclic shift is determined based on the one-to-one mapping.

The first transmitter 102 a is configured to transmit the first ternarysequence to a first set of receivers. The first set of receivers isassociated with the first transmitter 102 a. The first set of receiversincludes the first coherent receiver 104 a and the first non-coherentreceiver 104 b. The second transmitter 102 b is configured to transmitthe second ternary sequence to a second set of receivers. The second setof receivers is associated with the second transmitter 102 b. The secondset of receivers includes the second coherent receiver 104 c and thesecond non-coherent receiver 104 d.

The first set of receivers is configured to receive the first ternarysequence transmitted from the first transmitter 102 a. The second set ofreceivers is configured to receive the second ternary sequencetransmitted from the second transmitter 102 b. The first coherentreceiver 104 a is configured to demodulate the first ternary sequence bycorrelating the received first ternary sequence with all cyclic shiftsof a conjugate sequence obtained from the first base ternary sequence.In one example, the conjugate sequence is obtained by replacing numeric‘0’ with numeric ‘−1’.

The first non-coherent receiver 104 b is configured to demodulate thefirst ternary sequence by correlating the received first ternarysequence with all cyclic shifts of a conjugate sequence obtained from anabsolute value of the first base ternary sequence.

The second coherent receiver 104 c is configured to demodulate thesecond ternary sequence by correlating the received second ternarysequence with all cyclic shifts of a conjugate sequence obtained fromthe second base ternary sequence. The second non-coherent receiver 104 dis configured to demodulate the second ternary sequence by correlatingthe received second ternary sequence with all cyclic shifts of aconjugate sequence obtained from an absolute value of the second baseternary sequence. In one example, the absolute value of the first baseternary sequence and the absolute value of the second base ternarysequence are obtained by replacing numeric ‘−1’ of the first baseternary sequence and numeric ‘−1’ of the second base ternary sequencewith numeric ‘1’.

In one example, the first set of receivers is configured to detect atleast one data-symbol transmitted from the first transmitter 102 a byidentifying a first single cyclic shift corresponding to a maximumcorrelation value among all cyclic shifts.

In one example, the second set of receivers is configured to detect atleast one data-symbol transmitted from the second transmitter 102 b byidentifying a second single cyclic shift corresponding to a maximumcorrelation value among all cyclic shifts.

The first set of receivers is further configured to obtain each of theat least one data-symbol corresponding to the first transmitter 102 afrom the first single cyclic shift. The second set of receivers isfurther configured to obtain each of the at least one data-symbolcorresponding to the second transmitter 102 b from the second singlecyclic shift. The first set of receivers and the second set of receiversare configured to map the first single cyclic shift and the secondsingle cyclic shift to the corresponding data-symbols using an inverseof the one-to-one mapping that is applied to the respectivetransmitters.

The communication system 100 is designed such that each of thetransmissions is reliably decoded at each coherent receiver, forexample, the first coherent receiver 104 a or the second coherentreceiver 104 c, and each non-coherent receiver, for example, the firstnon-coherent receiver 104 b or the second non-coherent receiver 104 d.The interference between the two transmissions decreases.

In an example in which information bits from a higher layer to betransmitted are packed into k bit blocks, where each block represents adata-symbol drawn from an M-ary alphabet, data-symbol S, is representedas Equation 1.S={0,1,2, . . . , M−1}, M=2^(k)  [Equation 1]

Here, an information rate is represented using k bits/symbol. Eachdata-symbol is mapped to ternary sequences obtained from a ternarycodeset. In this context, the ternary codeset includes a set of ternarysequences. Let C¹ denote a ternary codeset from which the ternarysequences are assigned to data-symbols corresponding to the firsttransmitter 102 a and C² denote a ternary from which the ternarysequences are assigned to data-symbols corresponding to the secondtransmitter 102 b. Thus, before transmission, each data-symbol from S ismapped to one of M possible sequences or codewords from each codeset.Each of the ternary codes C^(n), n−1, 2 includes M≥2^(k) sequences,each, of period N. The mapping is represented as Equation 2.m ∈S

c _(m) ∈C ^(n) , n=1,2  [Equation 2]

Although FIG. 1 illustrates an example of components of thecommunication system 100, it is to be understood that other examples maybe implemented. In other examples, the communication system 100 mayinclude a less or a greater number of structural components than thoseillustrated and described with respect to FIG. 1. Further, labels ornames of the structural components are used only for illustrativepurpose and do not limit the scope of the examples. One or morestructural components may be combined together to perform the same orsubstantially similar function in the communication system 100.

FIG. 2 illustrates an example of various operations at a transmitter,for example, the first transmitter 102 a and the second transmitter 102b, a coherent receiver, for example, the first coherent receiver 104 aand the second coherent receiver 104 c. The communication system 100also includes a non-coherent receiver, for example, the firstnon-coherent receiver 104 b and the second non-coherent receiver 104 d.Data-symbol mapping operations at various stages, for example, anoperation at the first transmitter 102 a or the second transmitter 102b, an operation at the first coherent receiver 104 a or the secondcoherent receiver 104 c, and an operation at the first non-coherentreceiver 104 b or the second non-coherent receiver 104 d, in thecommunication system 100 will be described with reference to FIG. 2.Here, a transmitted ternary sequence is c_(m) ∈ C^(n), n=1, 2 for anyparticular transmission from one of the first transmitter 102 a and thesecond transmitter 102 b.

Transmitted ternary sequences are received at all of the receivers, forexample, the first coherent receiver 104 a, the first non-coherentreceiver 104 b, the second coherent receiver 104 c, and the secondnon-coherent receiver 104 d, corresponding to the first transmitter 102a and the second transmitter 102 b, respectively. Hereinafter,operations at the first coherent receiver 104 a or the second coherentreceiver 104 c and the first non-coherent receiver 104 b or the secondnon-coherent receiver 104 d are described.

Coherent reception: Let r=[r[0], . . . , r[N−1]^(†) be a receivedsequence corrupted by additive white Gaussian noise (AWGN). Adata-symbol estimate {circumflex over (m)} ∈ S for coherent reception atthe first coherent receiver 104 a or the second coherent receiver 104 cis given by a maximum likelihood (ML) detection, and expressed byEquation 3.

$\begin{matrix}{\hat{m} = {\underset{m\;{\epsilon{({0,1,\;\ldots\;,M})}}}{\arg\;\max}r^{\dagger}\left\{ c_{m} \right\}^{b}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

In Equation 3, { }^(b) denotes an operator that replaces ‘0’ in with‘−1’. This helps in obtaining better correlation properties as discussedlater.

Non-coherent reception: Estimates of transmitted ternary sequences areobtained at the first non-coherent receiver 104 b or the secondnon-coherent receiver 104 d and expressed by Equation 4.

$\begin{matrix}{\hat{m} = {\underset{m \in {\{{0,\; 1,\;\ldots\;,M}\}}}{\arg\;\max}{r}^{\dagger}\left\{ {c_{m}} \right\}^{b}}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

In Equation 4, |r| represents an absolute value operation on theindividual elements of r. A sequence {|c_(m)|}^(b) is obtained byinitially performing the absolute value operation on the individualelements c_(m) and subsequently replacing ‘0’ with ‘−1’ in the resultingsequence.

Embodiment or configuration requirements of ternary codesets c^(n), n=1,2: Based on the operation at the first transmitter 102 a or the secondtransmitter 102 b, the operation at the first coherent receiver 104 a orthe second coherent receiver 104 c, and the operation at the firstnon-coherent receiver 104 b or the second non-coherent receiver 104 d,the requirements on the ternary code design may be described as follows.

The coherent correlation for any pair of sequences drawn from the samecodeset or different codesets is low or as low as possible.

The non-coherent correlation for any pair of sequences drawn from thesame codeset or different codesets is low or as low as possible.

Here, the coherent correlation (CC) and the non-coherent correlation(NCC) are to be low or as low as possible. For c_(i),c_(j), a CCfunction R_(ci,cj) ^(c)(k) and an NCC function R_(ci,cj) ^(nc)(k) aredefined as Equation 5 and Equation 6, respectively.

$\begin{matrix}{{R_{c_{i},c_{j}}^{c}(k)} = {\sum\limits_{n = 0}^{N - 1}{{c_{i}\lbrack n\rbrack}\left\{ {c_{j}\left\lbrack {\left( {n + k} \right)\;{mod}\; N} \right\rbrack} \right\}^{b}}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack \\{{R_{c_{i},c_{j}}^{nc}(k)} = {\sum\limits_{n = 0}^{N - 1}{{{c_{i}\lbrack n\rbrack}}\left\{ {{c_{j}\left\lbrack {\left( {n + k} \right)\;{mod}\; N} \right\rbrack}} \right\}^{b}}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

Here, N≥M corresponds to a length/period of the ternary sequences.Further, c_(i),c_(j) corresponds to the same set C¹ or C², or c_(i) ∈C¹,c_(j) ∈ C² and vice-versa. Also, in the definition of CC and NCC, thesequences c_(i) and c_(j) are interchangeably used.

Accordingly, configuring two ternary codesets C¹ and C² with goodintra-set and inter-set correlation properties as defined by Equation 5and Equation 6 may become an issue.

Embodiment or configuration of ternary codesets C^(n), n=1, 2: Theembodiment or configuration of ternary codesets C^(n), n=1, 2 involvesconfiguring two base ternary sequences with good autocorrelationproperties individually and good cross-correlation propertiescollectively. The sets C¹ and C² are obtained as sets of cyclic shiftsof the two base ternary sequences. The base ternary sequences arerepresented as x and y with elements represented by μ_(x) and μ_(y),respectively. The codes C¹ and C² are given by Equation 7 and Equation8, respectively.C ¹ ={c _(i) :c _(i) =L ^(g){μ_(x) _(i) }, ∀g∈[0,N−1]}  [Equation 7]C ² ={c _(k) :c _(k) =L ^(g){μ_(y) _(k) },∀g∈[0,N−1]}  [Equation 8]

The sequence design issue lies in configuring the base ternary sequencesμ_(x) and μ_(y), with low values with respect to phase autocorrelationindividually and low correlation collectively. Hereinafter, theconfiguration of the ternary sequences μ_(x) and μ_(y), will bedescribed. In an embodiment, the configuration is based on maximallength sequences or m-sequences.

An m-sequence is a binary sequence assuming values from set {0,1}, anddefined for all periods P=2^(m)−1,m. Here, m denotes an integer.M-sequences may be generated using a Linear Feedback Shift Register(LFSR) with feedback polynomials selected as a primitive polynomial overthe field GF(2). The M-sequence corresponds to the maximum period thatis obtained from an LFSR of a given length.

Example of preferred pair of m-sequences:

For any pair of m-sequences x and y with period P, a cross-correlationfunction between x and y is defined for a lag k, as expressed byEquation 9.

$\begin{matrix}{{{\theta_{({x,y})}\lbrack k\rbrack} = {\sum\limits_{n = 0}^{P - 1}\left( {- 1} \right)^{({x_{i\; \oplus}y_{{({i + k})}{mod}\; P}})}}},{0 \leq k < P}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

Let θ_((x,y))={θ_((x,y))[0], . . . , θ_((x,y))[P−1]} be the sequence ofcross-correlation functions for different lags.

A pair of m-sequences (x, y) with the period P=2{circumflex over ( )}n−1is defined as a preferred pair of m-sequences in a case of Equation 10.

$\begin{matrix}{{{\theta_{({x,y})}\lbrack k\rbrack} \in \left\{ {{- 1},{{- 1} \pm 2^{\frac{n + 1}{2}}}} \right)},{\forall{k \in \left\{ {0,\ldots\mspace{14mu},{P - 1}} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

In Equation 10, x denotes an m-sequence with period P−2^(n)−1 withelements represented as x=[x₀, x₁, . . . , x_(p−1)]. Then, a sequencey=x^((d)), obtained as the d-decimation of the sequence x, together forma preferred pair of m-sequences if d=2^(m)+1 and the integer

$m \leq \frac{k - 1}{2}$such that GCD(m,n)=1.

The following example is considered for the configuration of the ternarysequences.

Example 1

In an embodiment, the m-sequences x and y form a preferred pair withperiod P=2{circumflex over ( )}n−1. As described above, let x be them-sequence from which the m-sequence y is derived. Let ϕ[x] be a mappingdefined as Equation 11.

$\begin{matrix}{{\Phi\lbrack ɛ\rbrack} = \left\{ \begin{matrix}{0,{ɛ = 0}} \\{1,{ɛ \neq 0}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

Then, Φ[x] maps the sequence 1+θ_((x,y)) to the original m-sequence x,as expressed by Equation 12.Φ[1+θ(x,y)]=x  [Equation 12]

Elements of the m-sequence x are represented by Equation 13.x _(i) =Tr(γα^(i))  [Equation 13]

In Equation 13, Tr(ε) denotes a trace representation of element ε ∈GF(2^(n)) and is expressed by Equation 14.Tr(ε)=ε+ε²+ε² ² + . . . +ε² ^(n−1)   [Equation 14]

Also, α denotes a primitive element in GF(2^(n)). The element γ ∈GF*(2^(n)) determines an initial phase of the m-sequence and 2¹−1 phasescorresponds to γ ∈ GF*(2^(n)) that is different by 2^(n)−1. The initialphase is defined or fixed by letting γ=1 resulting in the characteristicphase of the m-sequence x and also the m-sequence y. The m-sequence y isobtained as the d-decimation of the m-sequence x. Here, d=2^(m)+1 andthe integer m≤k−1/2 such that D(m, n)−1. Also, other decimations mayyield three values of the cross-correlation function. The decimationsmay also be referred to as a predefined decimation as follows.y _(i) =x _(di) =Tr(α^(id))  [Equation 15]

The cross-correlation function of the m-sequences x and y at delay k isexpressed by Equation 16.

$\begin{matrix}{{{\theta_{({x,y})}\lbrack k\rbrack} = {\sum\limits_{n = 0}^{P - 1}\left( {- 1} \right)^{\{{{{Tr}{(\alpha^{id})}} \oplus {{Tr}{({\alpha^{i}\alpha^{k}})}}}\}}}},{0 < k < P}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

Gold demonstrated that the cross-correlation function θ_((x,y))[k] at anarbitrary delay k depends on a k^(th) element, for example,

x

_k, of the m-sequence x, as expressed by Equation 17.

$\begin{matrix}{{\theta_{({x,y})}\lbrack k\rbrack} = \left\{ \begin{matrix}{{- 1},{x_{k} = 0}} \\{{{- 1} \pm 2^{\frac{n + 1}{2}}},{x_{k} = 1}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack\end{matrix}$

A result of adding ‘1’ to θ_((x,y))[k],∀ k ∈ {0,P−1} is expressed byEquation 18.

$\begin{matrix}{{1 + {\theta_{({x,y})}\lbrack k\rbrack}} = \left\{ {\begin{matrix}{0,{x_{k} = 0}} \\{{\pm 2^{\frac{n + 1}{2}}},{x_{k} = 1}}\end{matrix},{\forall{k \in \left\{ {0,1,{P - 1}} \right\}}}} \right.} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack\end{matrix}$

A result of mapping ϕ[ε] to (1+θ_((x,y))[k]) is expressed by Equation19.

$\begin{matrix}{{\Phi\left\lbrack {1 + {\theta_{({x,y})}\lbrack k\rbrack}} \right\rbrack} = \left\{ \begin{matrix}{0,{x_{k} = 0}} \\{1,{x_{k} = 1}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack\end{matrix}$

Thus, the sequence ϕ[1+θ(x,y)[k]] is the same as the m-sequence x, andis expressed by Equation 20.Φ[1+θ(x,y)]=x  [Equation 20]

Any pair of ideal two-level autocorrelation sequences θ and μ aredefined by a property of sequence ψ^((θ,μ)) of which elements areexpressed by Equation 21.ψ_(k) ^((θ,μ))=1=θ(θ,μ)[k]  [Equation 21]

Equation 21 is a perfect non-binary sequence characterized by zeroout-of-phase autocorrelation, which is expressed by Equation 22.

$\begin{matrix}{{{R\left( \psi_{k}^{({\vartheta,\mu})} \right)}\lbrack k\rbrack} = {{\sum\limits_{n = 0}^{P - 1}{\psi_{n}^{({\vartheta,\mu})}\psi_{n + k}^{({\vartheta,\mu})}}} = \left\{ {\begin{matrix}{{\psi_{k}^{({\vartheta,\mu})}},{n = 0}} \\{0,{0 < n < P}}\end{matrix},} \right.}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

In Equation 22, |ψ_(k) ^((θ,μ))| denotes a norm of a sequence obtainedas a dot product

ψ^((θ,μ)).ψ^((θ,μ))

.

FIG. 3 is a flowchart illustrating an example of a method 300 totransmit independent data from at least two transmitters tocorresponding at least two receivers, in accordance with an embodiment.

Referring to FIG. 3, in operation 302, the method 300 includes obtaininga first ternary sequence from a first base ternary sequencecorresponding to a first set of data-symbols. In one example, the method300 configures the first transmitter 102 a to obtain the first ternarysequence from the first base ternary sequence corresponding to the firstset of data-symbols. The first set of data-symbols has a predefinedlength.

In operation 304, the method 300 includes obtaining a second ternarysequence from a second base ternary sequence corresponding to a secondset of data-symbols. The second set of data-symbols has the predefinedlength. In one example, the method 300 enables the second transmitter102 b to obtain the second ternary sequence from the second base ternarysequence, corresponding to the second set of data-symbols. In operation306, the method 300 includes transmitting the first ternary sequence toa first set of receivers. The first set of receivers is associated withthe first transmitter 102 a. In operation 308, the method 300 includestransmitting the second ternary sequence to a second set of receivers.The second set of receivers is associated with or corresponds to thesecond transmitter 102 b. In one example, the method 300 enables thesecond transmitter 102 b to transmit the second ternary sequence to thesecond set of receivers.

The various actions, functions, blocks, operations illustrated anddescribed with respect to the method 300 may be performed in orderpresented, in different order, or simultaneously. Further, in someexamples, some of the actions, functions, blocks, operations, and thelike may be omitted, added, modified, skipped, and the like, withoutdeparting from the scope of the examples.

FIG. 4A is a flowchart illustrating an example of a method 400 a toobtain a first base ternary sequence, in accordance with an embodiment.

Referring to FIG. 4A, in operation 402 a, the method 400 a includesobtaining a first m-sequence of a period N−1.

In operation 404 a, the method 400 a includes obtaining a first perfectternary sequence from the first m-sequence. In operation 406 a, themethod 400 a includes appending a zero to a run of all zeros in thefirst perfect ternary sequence. That is, a new zero is appended to therun of all zeros in the first perfect ternary sequence. For example, anew zero is appended at a front of the run of all zeros in the firstperfect ternary sequence. As another example, a new zero is appended atrear of the run of all zeros in the first perfect ternary sequence. Inan alternative example, a new zero is inserted between the run of allzeros in the first perfect ternary sequence. For example, upon the firstperfect ternary sequence being “001111”, the appending the zero to therun of all zeros in the first perfect ternary sequence is “10001111”.

In operation 408 a, the method 400 a includes obtaining the first baseternary sequence. The first transmitter 102 a and the second transmitter102 b retrieve the respective base ternary sequences.

The various actions, functions, blocks, operations, and the like in themethod 400 a may be performed in order presented, in different order, orsimultaneously. Further, in some examples, some of the actions,functions, blocks, operations, and the like may be omitted, added,modified, skipped, and the like without departing from the scope of theexamples.

FIG. 4B is a flowchart illustrating an example of a method 400 b toobtain a second base ternary sequence, in accordance with an embodiment.

Referring to FIG. 4B, in operation 402 b, the method 400 b includesobtaining a second m-sequence of a period N−1 as a predefined decimationof the first m-sequence used to generate the first ternary sequence.

In operation 404 b, the method 400 b includes obtaining a second perfectternary sequence from the second m-sequence. That is, a new zero isappended to the run of all zeros in the second perfect ternary sequence.For example, a new zero is appended at front of the run of all zeros inthe second perfect ternary sequence. As another example, a new zero isappended at rear of the run of all zeros in the second perfect ternarysequence. In an alternative example, a new zero is inserted between therun of all zeros in the second perfect ternary sequence.

In operation 406 b, the method 400 b includes appending a zero to a runof all zeros in the second perfect ternary sequence. For example, if thesecond perfect ternary sequence is “1100111”, the appending the zero tothe run of all zeros in the second perfect ternary sequence is“110001111”. In operation 408 b, the method 400 b includes obtaining thesecond base ternary sequence.

The various actions, functions, blocks, operations, and the like in themethod 400 b may be performed in order presented, in different order, orsimultaneously. Further, in some examples, some of the actions,functions, blocks, operations, and the like may be omitted, added,modified, skipped, and the like without departing from the scope of theexamples.

FIG. 5A is a flowchart illustrating an example of a method 500 a togenerate a first perfect ternary sequence, in accordance with anembodiment.

Referring to FIG. 5A, in operation 502 a, the method 500 a includesobtaining a preferred pair of m-sequences from the first m-sequence. Inoperation 504 a, the method 500 a includes obtaining a first correlationsequence of the preferred pair. The correlation sequence is obtained asa cross-correlation function between two m-sequences of the preferredpair. In operation 506 a, the method 500 a includes obtaining a firstoffset correlation sequence from the first correlation sequence. Inoperation 508 a, the method 500 a includes generating the first perfectternary sequence based on the first offset correlation sequence.

The various actions, functions, blocks, operations, and the like in themethod 500 a may be performed in order presented, in different order, orsimultaneously. Further, in some examples, some of the actions,functions, blocks, operations, and the like may be omitted, added,modified, skipped, and the like without departing from the scope of theexamples.

FIG. 5B is a flowchart illustrating an example of a method 500 b togenerate a second perfect ternary sequence, in accordance with anembodiment.

Referring to FIG. 5B, in operation 502 b, the method 500 b includesobtaining a preferred pair of m-sequences from the second m-sequence. Inoperation 504 b, the method 500 b includes obtaining a secondcorrelation sequence of the preferred pair. The correlation sequence isobtained as a cross-correlation function between two m-sequences of thepreferred pair.

In operation 506 b, the method 500 b includes obtaining a second offsetcorrelation sequence from the second correlation sequence. In operation508 b, the method 500 b includes generating the second perfect ternarysequence based on the second offset correlation sequence.

The method 500 b may be employed to generate a perfect ternary sequencewith the period of the form P=2{circumflex over ( )}n−1, using preferredpairs of m-sequences. Let x corresponding to an m-sequence of period P,and y corresponding to an m-sequence obtained from the m-sequence y,using the decimation described earlier form the preferred pair, i.e.,(x, y). Using Example 1, elements of a cross-correlation sequenceinclude values as demonstrated in Equation 23.

$\begin{matrix}{{{\theta\left( {x,y} \right)}\lbrack k\rbrack} \in \left\{ {{- 1},{{- 1} \pm 2^{\frac{n + 1}{2}}}} \right\}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

Also, the sequence ψ^((x,y))=θ(x,y)+1 obtained by adding ‘1’ to eachelement of the cross-correlation function θ(x,y) is a perfect sequenceover a non-binary alphabet. The elements of ψ^((x,y)) assume values asshown in Equation 24.

$\begin{matrix}{\psi_{k}^{({x,y})} \in \left\{ {0,{\pm 2^{\frac{n + 1}{2}}}} \right\}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

By dividing the sequence

${\psi^{({x,y})} = {1 + {{\theta\left( {x,y} \right)}\mspace{14mu}{by}\mspace{14mu} 2^{\frac{n + 1}{2}}}}},$a perfect ternary sequence Λ(x,y) with elements is generated from{0,±1}. Such perfect ternary sequence Λ(x,y) is represented by Equation25.Φ[ψ^((x,y))]=|θ(x,y)|  [Equation 25]

Here, |Λ(x,y)| is obtained by replacing each element of the sequenceθ(x,y) with a corresponding absolute value, and, from Example 1, isshown in Equation 26.|Λ(x,y)|=x  [Equation 26]

Accordingly, the m-sequence x arrives at a ternary sequence with perfectcorrelation. Furthermore, zero and non-zero positions of the ternarysequence identify the starting m-sequence x. Hereinafter, the perfectternary sequence θ(x,y) may also be referred as v_(x) for notationalconvenience.

Hereinafter, design methodology will be described.

In accordance with an embodiment, the sequence design uses an m-sequenceof period P=2^(n)=1 to produce a pair of ternary sequences of periodN=2^(n). Balanced sequences are generated that include the same numberof zero and non-zero elements. In accordance with an example:

The m-sequence x of period P=N−1=2^(n)−1 is obtained.

The perfect ternary sequence v_(x) of period P is obtained from them-sequence x using procedure A.

The m-sequence y with elements y_(i)=x_(di)=Tr(α^(id)) is obtained.Here, d=2^(m)+1 and the integer

$m \leq \frac{k - 1}{2}$such that GCD(m,n)=1.

The perfect ternary sequence v_(y) of the period P is obtained from them-sequence y using the procedure A.

In one example, ‘0’ is appended to the run of all zeros of lengthlog₂N−1 in each of the ternary sequences v_(x) and v_(y) to obtain apair of ternary sequences (μ_(x), μ_(y)).

Through this, two ternary sequences μ_(x) and μ_(y) with low values ofcross-correlation across both binary alphabet {0, 1} and ternaryalphabet {0, ±1} are obtained.

FIG. 6 is a flowchart illustrating an example of a method 600 toidentify data represented by a received ternary sequence at a set ofreceivers, in accordance with an embodiment.

Referring to FIG. 6, in operation 602, the method 600 includes receivinga first ternary sequence or a second ternary sequence transmitted fromthe first transmitter 102 a or the second transmitter 102 b,respectively. In one example, the method 600 enables a first set ofreceivers or a second set of receivers to receive the first ternarysequence or the second ternary sequence transmitted from the firsttransmitter 102 a or the second transmitter 102 b, respectively.

In operation 604 a, the method 600 includes demodulating the firstternary sequence by correlating the received first ternary sequence withall cyclic shifts of a conjugate sequence obtained from the first baseternary sequence. In one example, the method 600 enables the firstcoherent receiver 104 a to demodulate the first ternary sequence bycorrelating the received first ternary sequence with all cyclic shiftsof the conjugate sequence obtained from the first base ternary sequence.In one example, the conjugate sequence is obtained by replacing numeric‘0’ with numeric ‘−1’.

In operation 604 b, the method 600 includes demodulating the firstternary sequence by correlating the received first ternary sequence withall cyclic shifts of a conjugate sequence obtained from an absolutevalue of the first base ternary sequence. In one example, the method 600enables the first non-coherent receiver 104 b to demodulate the firstternary sequence by correlating the received first ternary sequence withall cyclic shifts of the conjugate sequence obtained from the absolutevalue of the first base ternary sequence.

In operation 606 a, the method 600 includes demodulating the secondternary sequence by correlating the received second ternary sequencewith all cyclic shifts of a conjugate sequence, which is obtained fromthe second base ternary sequence. In one example, the method 600 enablesthe second coherent receiver 104 c to demodulate the second ternarysequence by correlating the received second ternary sequence with allcyclic shifts of the conjugate sequence obtained from the second baseternary sequence.

In operation 606 b, the method 600 includes demodulating the secondternary sequence by correlating the received second ternary sequencewith all cyclic shifts of a conjugate sequence obtained from an absolutevalue of the second base ternary sequence. In one example, the method600 enables the second non-coherent receiver 104 d to demodulate thesecond ternary sequence by correlating the received second ternarysequence with all cyclic shifts of conjugate sequence obtained from theabsolute value of the second base ternary sequence.

In an example, the absolute value of the first base ternary sequence andthe absolute value of the second base ternary sequence are obtained byreplacing numeric ‘−1’ of the first base ternary sequence and numeric‘−1’ of the second base ternary sequence with numeric ‘1’.

In operation 608, the method 600 includes detecting a data-symboltransmitted from the first transmitter 102 a or the second transmitter102 b. In one example, the method 600 allows the first set of receiversto detect the data-symbol transmitted from the first transmitter 102 aby identifying a first single cyclic shift corresponding to a maximumcorrelation value among all cyclic shifts. In one example, the method600 enables the second set of receivers to detect the data-symboltransmitted from the second transmitter 102 b by identifying a secondsingle cyclic shift corresponding to a maximum correlation value amongall cyclic shifts.

In operation 610, the method 600 includes obtaining the data-symbolcorresponding to the first transmitter 102 a or the second transmitter102 b from the first single cyclic shift or the second single cyclicshift using an inverse of the one-to-one mapping. In one example, themethod 600 enables the first set of receivers to obtain the data-symbolcorresponding to the first transmitter 102 a from the first singlecyclic shift using the inverse of the one-to-one mapping. In oneexample, the method 600 enables the second set of receivers to obtainthe data-symbol corresponding to the second transmitter 102 b from thesecond single cyclic shift using the inverse of the one-to-one mapping.

The various actions, functions, blocks, operations, and the like in themethod 600 may be performed in order presented, in different order, orsimultaneously. Further, in some examples, some of the actions,functions, blocks, operations, and the like may be omitted, added,modified, skipped, and the like without departing from the scope of theexamples.

FIGS. 7A and 7B are graphs showing examples of an autocorrelationproperty of a first base ternary sequence, in accordance with anembodiment. Here, a base ternary sequence of length 128 is selected todemonstrate correlation properties.

FIGS. 8A and 8B are graphs showing examples of an autocorrelationproperty of a second base ternary sequence, in accordance with anembodiment. Here, a base ternary sequence of length 128 is selected todemonstrate correlation properties.

Referring to FIGS. 7A and 7B, and FIGS. 8A and 8B, values ofout-of-phase autocorrelation are low for sequences in both coherent andnon-coherent scenarios.

FIGS. 9A and 9B are graphs showing examples of a correlation between afirst base ternary sequence and a second ternary sequence, each having alength of 128. Referring to FIGS. 9A and 9B, a cross-correlation betweenthe two sequences is also better for both coherent reception andnon-coherent reception.

Table 1 shows sequences μ_(x) and μ_(y) for periods 8, 32, and 128,according to some examples.

TABLE 1 N Ternary sequence μ_(x) Ternary sequence μ_(y) 8 100 0-11101-1000101 32 −100000-1010-1-11011000- −100-100-1100000-10110-1010001-11-11100110100 1101111 128 1001001-1010011-1-11111-1101-1-101-1011-1-10- 101110000111-1-1-1-10100010-1100101-1-1-1-1000- 0011101-100010100101-10000000-11001-101100011-10011- 111-10-10-10-1000 010-10-10-11-10000100-1-100000- 1101-111001-1-10010- 1010101-1010010010-100-101100-11000001-10-110- 1111001000-11010-10000 101-110-1000-1-100-1000-10000000

The sequences presented in Table 1 are used to encode data-symbols fortransmission over a wireless channel. Each of the first transmitter 102a and the second transmitter 102 b of FIG. 1 selects one of the twosequences in Table 1 and uses each ternary sequence for transmission ofinformation to each receiver, for example, the first coherent receiver104 a, the first non-coherent receiver 104 b, the second coherentreceiver 104 c, and the second non-coherent receiver 104 d. Because therespective spreading sequences to encode data-symbols are obtained ascyclic shifts of a single sequence in the following Table 2, a number ofdistinct spreading sequences is equal to a spreading factor itself.Thus, the spreading sequences of spreading factor M are used to encodedata-symbols of size k=log₂M. For example, spreading sequences ofspreading factor M=8 encode data-symbols with size k=log₂8=3. Similarly,spreading sequences with spreading factors 32 and 128 are used to encodedata-symbols of sizes 5 and 7, respectively. Depending on applications,spreading codes are assigned to data-symbols based on any customizedlogic, for example, grey coding.

In Table 2, an example of assigning spreading codes to data-symbols fork=3 and M=8 is presented. Here, cyclic shifts given to the originalsequence are decimal equivalent of a binary data-symbol, which is theone-to-one mapping that determines a cyclic shift of a base ternarysequence for a given data-symbol at transmitters. For example, in Table2, a cyclic shift is 1 for data-symbol 001. For the method of assigningcyclic shifts of a base ternary sequence to data-symbols some variationsmay be made.

TABLE 2 Cyclic shift Data-symbol (Decimal equivalent ) Base ternarysequence 000 0 1000-1110 001 1 01000-111  010 2 101000-11   011 31101000-1    100 4 −11101000 101 5    0-1110100 110 6   00-111010 111 70 00-11101

Table 2 is used to obtain the inverse of the one-to-one mapping atreceivers. For example, the cyclic shift of 1 determined at any receiveris mapped to the data-symbol 001.

The first transmitter 102 a, the second transmitter 102 b, the firstnon-coherent receiver 104 b, the first coherent receiver 104 a, thesecond non-coherent receiver 104 d, and the second coherent receiver 104c in FIGS. 1 and 2 that perform the operations described in thisapplication are implemented by hardware components configured to performthe operations described in this application that are performed by thehardware components. Examples of hardware components that may be used toperform the operations described in this application where appropriateinclude controllers, sensors, generators, drivers, memories,comparators, arithmetic logic units, adders, subtractors, multipliers,dividers, integrators, and any other electronic components configured toperform the operations described in this application. In other examples,one or more of the hardware components that perform the operationsdescribed in this application are implemented by computing hardware, forexample, by one or more processors or computers. A processor or computermay be implemented by one or more processing elements, such as an arrayof logic gates, a controller and an arithmetic logic unit, a digitalsignal processor, a microcomputer, a programmable logic controller, afield-programmable gate array, a programmable logic array, amicroprocessor, or any other device or combination of devices that isconfigured to respond to and execute instructions in a defined manner toachieve a desired result. In one example, a processor or computerincludes, or is connected to, one or more memories storing instructionsor software that are executed by the processor or computer. Hardwarecomponents implemented by a processor or computer may executeinstructions or software, such as an operating system (OS) and one ormore software applications that run on the OS, to perform the operationsdescribed in this application. The hardware components may also access,manipulate, process, create, and store data in response to execution ofthe instructions or software. For simplicity, the singular term“processor” or “computer” may be used in the description of the examplesdescribed in this application, but in other examples multiple processorsor computers may be used, or a processor or computer may includemultiple processing elements, or multiple types of processing elements,or both. For example, a single hardware component or two or morehardware components may be implemented by a single processor, or two ormore processors, or a processor and a controller. One or more hardwarecomponents may be implemented by one or more processors, or a processorand a controller, and one or more other hardware components may beimplemented by one or more other processors, or another processor andanother controller. One or more processors, or a processor and acontroller, may implement a single hardware component, or two or morehardware components. A hardware component may have any one or more ofdifferent processing configurations, examples of which include a singleprocessor, independent processors, parallel processors,single-instruction single-data (SISD) multiprocessing,single-instruction multiple-data (SIMD) multiprocessing,multiple-instruction single-data (MISD) multiprocessing, andmultiple-instruction multiple-data (MIMD) multiprocessing.

The methods illustrated in FIGS. 3 through 6 that perform the operationsdescribed in this application are performed by computing hardware, forexample, by one or more processors or computers, implemented asdescribed above executing instructions or software to perform theoperations described in this application that are performed by themethods. For example, a single operation or two or more operations maybe performed by a single processor, or two or more processors, or aprocessor and a controller. One or more operations may be performed byone or more processors, or a processor and a controller, and one or moreother operations may be performed by one or more other processors, oranother processor and another controller. One or more processors, or aprocessor and a controller, may perform a single operation, or two ormore operations.

Instructions or software to control computing hardware, for example, oneor more processors or computers, to implement the hardware componentsand perform the methods as described above may be written as computerprograms, code segments, instructions or any combination thereof, forindividually or collectively instructing or configuring the one or moreprocessors or computers to operate as a machine or special-purposecomputer to perform the operations that are performed by the hardwarecomponents and the methods as described above. In one example, theinstructions or software include machine code that is directly executedby the one or more processors or computers, such as machine codeproduced by a compiler. In another example, the instructions or softwareincludes higher-level code that is executed by the one or moreprocessors or computer using an interpreter. The instructions orsoftware may be written using any programming language based on theblock diagrams and the flow charts illustrated in the drawings and thecorresponding descriptions in the specification, which disclosealgorithms for performing the operations that are performed by thehardware components and the methods as described above.

The instructions or software to control computing hardware, for example,one or more processors or computers, to implement the hardwarecomponents and perform the methods as described above, and anyassociated data, data files, and data structures, may be recorded,stored, or fixed in or on one or more non-transitory computer-readablestorage media. Examples of a non-transitory computer-readable storagemedium include read-only memory (ROM), random-access memory (RAM), flashmemory, CD-ROMs, CD-Rs, CD+Rs, CD-RWs, CD+RWs, DVD-ROMs, DVD-Rs, DVD+Rs,DVD-RWs, DVD+RWs, DVD-RAMs, BD-ROMs, BD-Rs, BD-R LTHs, BD-REs, magnetictapes, floppy disks, magneto-optical data storage devices, optical datastorage devices, hard disks, solid-state disks, and any other devicethat is configured to store the instructions or software and anyassociated data, data files, and data structures in a non-transitorymanner and provide the instructions or software and any associated data,data files, and data structures to one or more processors or computersso that the one or more processors or computers can execute theinstructions. In one example, the instructions or software and anyassociated data, data files, and data structures are distributed overnetwork-coupled computer systems so that the instructions and softwareand any associated data, data files, and data structures are stored,accessed, and executed in a distributed fashion by the one or moreprocessors or computers.

While this disclosure includes specific examples, it will be apparentafter an understanding of the disclosure of this application thatvarious changes in form and details may be made in these exampleswithout departing from the spirit and scope of the claims and theirequivalents. The examples described herein are to be considered in adescriptive sense only, and not for purposes of limitation. Descriptionsof features or aspects in each example are to be considered as beingapplicable to similar features or aspects in other examples. Suitableresults may be achieved if the described techniques are performed in adifferent order, and/or if components in a described system,architecture, device, or circuit are combined in a different manner,and/or replaced or supplemented by other components or theirequivalents. Therefore, the scope of the disclosure is defined not bythe detailed description, but by the claims and their equivalents, andall variations within the scope of the claims and their equivalents areto be construed as being included in the disclosure.

What is claimed is:
 1. A method to transmit independent data by acommunication system including one or more processors, a firsttransmitter, and a second transmitter, the method comprising: obtaining,using the one or more processors, a first perfect ternary sequence and asecond perfect ternary sequence based on a first m-sequence; obtaining,using the one or more processors, a first base ternary sequence based onthe first perfect ternary sequence; obtaining, using the one or moreprocessors, a second base ternary sequence based on the second perfectternary sequence; obtaining, using the one or more processors, a firstternary sequence from the first base ternary sequence corresponding to afirst set of data-symbols; obtaining, using the one or more processors,a second ternary sequence from the second base ternary sequencecorresponding to a second set of data-symbols; transmitting, from thefirst transmitter, the first ternary sequence to a first set ofreceivers associated with the first transmitter; and transmitting, fromthe second transmitter, the second ternary sequence to a second set ofreceivers associated with the second transmitter.
 2. The method of claim1, wherein the first base ternary sequence comprises a predefined lengthand retrieved at the first transmitter.
 3. The method of claim 1,wherein the second base ternary sequence comprises a predefined lengthand is retrieved at the second transmitter.
 4. The method of claim 1,wherein the first ternary sequence is obtained as a cyclic shift of thefirst base ternary sequence, and the cyclic shift corresponds to adata-symbol to be transmitted from the first transmitter and isdetermined based on a one-to-one mapping.
 5. The method of claim 1,wherein the second ternary sequence is obtained as a cyclic shift of thesecond base ternary sequence, and the cyclic shift corresponds to adata-symbol to be transmitted from the second transmitter and isdetermined based on a one-to-one mapping.
 6. The method of claim 1,wherein the first base ternary sequence is generated by: obtaining thefirst m-sequence of a period N−1; obtaining the first perfect ternarysequence from the first m-sequence; and appending a zero to a run of allzeros in the first perfect ternary sequence.
 7. The method of claim 1,wherein the second base ternary sequence is generated by: obtaining asecond m-sequence of a period N−1 as a decimation of the firstm-sequence used to generate the first ternary sequence; obtaining thesecond perfect ternary sequence from the second m-sequence; andappending a zero to a run of all zeros in the second perfect ternarysequence.
 8. The method of claim 6, wherein the first perfect ternarysequence is generated from the first m-sequence by: obtaining apreferred pair of m-sequences from the first m-sequence; obtaining afirst correlation sequence of the preferred pair, the correlationsequence being obtained as a cross-correlation function between twom-sequences of the preferred pair; obtaining a first offset correlationsequence from the first correlation sequence; and generating the firstperfect ternary sequence based on the first offset correlation sequence.9. The method of claim 7, wherein the second perfect ternary sequence isgenerated from the second m-sequence by: obtaining a preferred pair ofm-sequences from the second m-sequence; obtaining a second correlationsequence of the preferred pair, the correlation sequence being obtainedas a cross-correlation function between two m-sequences of the preferredpair; obtaining a second offset correlation sequence from the secondcorrelation sequence; and generating the second perfect ternary sequencebased on the second offset correlation sequence.
 10. The method of claim1, wherein the communication system includes the first set of receiversand the second set of receivers, wherein the first set of receiverscomprises a first non-coherent receiver and a first coherent receiverassociated with the first transmitter, and the second set of receiverscomprises a second non-coherent receiver and a second coherent receiverassociated with the second transmitter.
 11. The method of claim 10,further comprising: receiving, at the first set of receivers, the firstternary sequence transmitted from the first transmitter; receiving, atthe second set of receivers, the second ternary sequence transmittedfrom the second transmitter; demodulating, at the first coherentreceiver, the first ternary sequence by correlating the first ternarysequence with all cyclic shifts of a conjugate sequence obtained fromthe first base ternary sequence; and demodulating, at the firstnon-coherent receiver, the first ternary sequence by correlating thefirst ternary sequence with all cyclic shifts of a conjugate sequenceobtained from an absolute value of the first base ternary sequence. 12.The method of claim 10, further comprising: demodulating, at the secondcoherent receiver, the second ternary sequence by correlating the secondternary sequence with all cyclic shifts of a conjugate sequence obtainedfrom the second base ternary sequence; and demodulating, at the secondnon-coherent receiver, the second ternary sequence by correlating thesecond ternary sequence with all cyclic shifts of a conjugate sequenceobtained from an absolute value of the second base ternary sequence. 13.The method of claim 4, wherein the communication system includes thefirst set of receivers and the second set of receivers, the methodfurther comprising: detecting, at the first set of receivers, adata-symbol transmitted from the first transmitter by identifying afirst single cyclic shift corresponding to a maximum correlation valueamong all cyclic shifts; detecting, at the second set of receivers, adata-symbol transmitted from the second transmitter by identifying asecond single cyclic shift corresponding to the maximum correlationvalue among all cyclic shifts; obtaining, at the first set of receivers,each of the data-symbols corresponding to the first transmitter from thefirst single cyclic shift using an inverse of the one-to-one mapping;and obtaining, at the second set of receivers, each of the data-symbolscorresponding to the second transmitter from the second single cyclicshift using the inverse of the one-to-one mapping.
 14. The method ofclaim 11, wherein the conjugate sequence is obtained by replacingnumeric ‘0’ with numeric ‘−1’ in the first base ternary sequence. 15.The method of claim 11, wherein the absolute value of the first baseternary sequence and an absolute value of the second base ternarysequence are obtained by replacing numeric ‘−1’ of the first baseternary sequence and by replacing numeric ‘−1’ of the second baseternary sequence with numeric ‘1’.
 16. The method of claim 1, whereindata to be transmitted is divided into the first set of data-symbolswith a predefined length and the second set of data-symbols with thepredefined length.
 17. A system for transmitting independent data,comprising: one or more processors configured to: obtain, using the oneor more processors, a first perfect ternary sequence and a secondperfect ternary sequence based on a first m-sequence; obtain, using theone or more processors, a first base ternary sequence based on the firstperfect ternary sequence; obtain, using the one or more processors, asecond base ternary sequence based on the second perfect ternarysequence; obtain a first ternary sequence from a first base ternarysequence corresponding to a first set of data-symbols; and obtain asecond ternary sequence from a second base ternary sequencecorresponding to a second set of data-symbols; a first transmitterconfigured to transmit the first ternary sequence to a first set ofreceivers associated with the first transmitter; and a secondtransmitter configured to transmit the second ternary sequence to asecond set of receivers associated with the second transmitter.
 18. Thesystem of claim 17, wherein the first base ternary sequence comprises apredefined length retrieved at the first transmitter.
 19. The system ofclaim 17, wherein the second base ternary sequence comprises thepredefined length retrieved at the second transmitter.
 20. The system ofclaim 17, wherein the first ternary sequence is obtained as a cyclicshift of the first base ternary sequence, and the cyclic shiftcorresponds to a data-symbol to be transmitted from the firsttransmitter and is determined based on a one-to-one mapping.
 21. Thesystem of claim 17, wherein the second ternary sequence is obtained as acyclic shift of the second base ternary sequence, and the cyclic shiftcorresponds to a data-symbol to be transmitted from the secondtransmitter and is determined based on a one-to-one mapping.
 22. Thesystem of claim 17, wherein the first base ternary sequence is generatedby obtaining the first m-sequence of a period N−1, obtaining the firstperfect ternary sequence from the first m-sequence, and appending a zeroto a run of all zeros in the first perfect ternary sequence.
 23. Thesystem of claim 17, wherein: the second base ternary sequence isgenerated by obtaining a second m-sequence of a period N−1 as adecimation of the first m-sequence used to generate the first ternarysequence, obtaining the second perfect ternary sequence from the secondm-sequence, and appending a zero to a run of all zeros in the secondperfect ternary sequence.
 24. The system of claim 22, wherein the firstperfect ternary sequence is generated from the first m-sequence byobtaining a preferred pair of m-sequences from the first m-sequence,obtaining a first correlation sequence of the preferred pair, thecorrelation sequence being obtained as a cross-correlation functionbetween two m-sequences of the preferred pair, obtaining a first offsetcorrelation sequence from the first correlation sequence, and generatingthe first perfect ternary sequence based on the first offset correlationsequence.
 25. The system of claim 23, wherein the second perfect ternarysequence is generated from the second m-sequence by obtaining apreferred pair of m-sequences from the second m-sequence, obtaining asecond correlation sequence of the preferred pair, the correlationsequence being obtained as a cross-correlation function between twom-sequences of the preferred pair, obtaining a second offset correlationsequence from the second correlation sequence, and generating the secondperfect ternary sequence based on the second offset correlationsequence.
 26. The system of claim 17, wherein the system furtherincludes the first set of receivers and the second set of receivers,wherein the first set of receivers comprises a first non-coherentreceiver and a first coherent receiver associated with the firsttransmitter, and the second set of receivers comprises a secondnon-coherent receiver and a second coherent receiver associated with thesecond transmitter.
 27. The system of claim 26, wherein the system isfurther configured to receive, using the first set of receivers, thefirst ternary sequence transmitted from the first transmitter, receive,using the second set of receivers, the second ternary sequencetransmitted from the second transmitter, demodulate, using the firstcoherent receiver, the first ternary sequence by correlating the firstternary sequence with all cyclic shifts of a conjugate sequence obtainedfrom the first base ternary sequence, and demodulate, using the firstnon-coherent receiver, the first ternary sequence by correlating thefirst ternary sequence with all cyclic shifts of a conjugate sequenceobtained from an absolute value of the first base ternary sequence. 28.The system of claim 26, wherein the system is further configured to:demodulate, using the second coherent receiver, the second ternarysequence by correlating the second ternary sequence with all cyclicshifts of a conjugate sequence obtained from the second base ternarysequence, and demodulate, using the second non-coherent receiver, thesecond ternary sequence by correlating the second ternary sequence withall cyclic shifts of a conjugate sequence obtained from an absolutevalue of the second base ternary sequence.
 29. The system of claim 20,wherein the system further includes the first set of receivers and thesecond set of receivers, wherein the system is further configured to:detect, using the first set of receivers, a data-symbol transmitted fromthe first transmitter by identifying a first single cyclic shiftcorresponding to a maximum correlation value among all cyclic shifts,detect, using the second set of receivers, a data-symbol transmittedfrom the second transmitter by identifying a second single cyclic shiftcorresponding to the maximum correlation value among all cyclic shifts,obtain, using the first set of receivers, each of the data-symbolscorresponding to the first transmitter from the first single cyclicshift, and obtain, using the second set of receivers, each of thedata-symbols corresponding to the second transmitter from the secondsingle cyclic shift using an inverse of the one-to-one mapping.
 30. Thesystem of claim 27, wherein the conjugate sequence is obtained byreplacing numeric ‘0’ with numeric ‘−1’ in the first base ternarysequence.
 31. The system of claim 27, wherein the absolute value of thefirst base ternary sequence and an absolute value of the second baseternary sequence are obtained by replacing numeric ‘−1’ of the firstbase ternary sequence and by replacing numeric ‘−1’ of the second baseternary sequence with numeric ‘1’.
 32. The system of claim 17, whereindata to be transmitted is divided into the first set of data-symbolswith a predefined length and the second set of data-symbols with thepredefined length.
 33. A method to receive independent data, the methodcomprising: a first coherent receiver configured to demodulate a firstternary sequence received from a first transmitter by correlating thefirst ternary sequence with all cyclic shifts of a conjugate sequenceobtained from a first base ternary sequence corresponding to a first setof data-symbols; a first non-coherent receiver configured to demodulatethe first ternary sequence by correlating the first ternary sequencewith all cyclic shifts of a conjugate sequence obtained from an absolutevalue of the first base ternary sequence; a second coherent receiverconfigured to demodulate a second ternary sequence received from asecond transmitter by correlating the second ternary sequence with allcyclic shifts of a conjugate sequence obtained from a second baseternary sequence corresponding to a second set of data-symbols; and asecond non-coherent receiver configured to demodulate the second ternarysequence by correlating the second ternary sequence with all cyclicshifts of a conjugate sequence obtained from an absolute value of thesecond base ternary sequence.
 34. The method of claim 33, wherein thefirst set of data-symbols is detected by identifying a first singlecyclic shift corresponding to a maximum correlation value among all ofthe cyclic shifts of the conjugate sequence obtained from the first baseternary sequence.
 35. The method of claim 33, wherein the second set ofdata-symbols is detected by identifying a second single cyclic shiftcorresponding to a maximum correlation value among all of the cyclicshifts of the conjugate sequence obtained from the second base ternarysequence.
 36. The method of claim 33, wherein the first set ofdata-symbols comprises a first predefined length and the second set ofdata-symbols comprises a second predefined length.